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Number of 2 X 2 matrices with entries in {0,1,...,n} and permanent = trace with no entry repeated.
2

%I #16 Dec 10 2016 22:37:47

%S 0,0,0,0,0,0,4,4,8,8,12,12,20,20,24,28,32,32,40,40,48,52,56,56,68,68,

%T 72,76,84,84,96,96,104,108,112,116,128,128,132,136,148,148,160,160,

%U 168,176,180,180,196,196,204

%N Number of 2 X 2 matrices with entries in {0,1,...,n} and permanent = trace with no entry repeated.

%C a(n) mod 4 = 0.

%H Indranil Ghosh and Chai Wah Wu, <a href="/A278933/b278933.txt">Table of n, a(n) for n = 0..10000</a> (terms for n = 0..285 from Indranil Ghosh)

%o (Python)

%o def t(n):

%o s=0

%o for a in range(0,n+1):

%o for b in range(0,n+1):

%o for c in range(0,n+1):

%o for d in range(0,n+1):

%o if (a!=b and a!=d and b!=d and c!=a and c!=b and c!=d):

%o if (a*d+b*c)==a+d:

%o s+=1

%o return s

%o for i in range(0,286):

%o print str(i)+" "+str(t(i))

%Y Cf. A210288 (wherein the entries can be repeated).

%K nonn

%O 0,7

%A _Indranil Ghosh_, Dec 02 2016